Subgroups — C₁₃×#33859 #15720198

Order 3328.

646 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3417	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3415	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3290	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2222	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2221	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2212	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2194	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2193	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2178	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#578	C₂²	1	2	yes	complemented
13	C₁₃×#577	—	2	2	no	—
14	C₁₃×#576	C₂²	1	2	yes	—
15	C₁₃×#510	—	2	2	no	—
16	C₁₃×#510	C₂²	1	2	yes	complemented
17	C₁₃×#509	—	2	2	no	—
18	C₁₃×#509	C₂²	1	2	yes	—
19	C₁₃×#508	—	2	1	no	—
20	C₁₃×#508	—	2	1	no	—
21	C₁₃×#508	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×Q₃₂	—	2	1	no	—
23	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
25	C₂×C₁₃×D₁₆	—	2	1	no	—
26	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
27	C₁₃×#504	C₂²	1	1	yes	characteristic
28	C₁₃×#504	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#495	C₂²	1	2	yes	complemented
30	C₁₃×#473	C₂²	1	2	yes	—
31	C₁₃×#472	C₂²	1	2	yes	complemented
32	C₁₃×#471	—	2	2	no	—
33	C₁₃×#455	—	2	2	no	—
34	C₁₃×#454	—	2	2	no	—
35	C₁₃×#443	C₂²	1	1	yes	characteristic
36	C₁₃×#443	C₂²	1	2	yes	complemented
37	C₁₃×#368	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#364	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#362	C₂²	1	2	yes	complemented
40	C₁₃×#361	C₂²	1	2	yes	complemented
41	C₁₃×#359	C₂²	1	2	yes	complemented
42	C₁₃×#350	C₂²	1	1	yes	characteristic
43	C₁₃×#350	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
45	C₁₃×2₋¹⁺⁴	—	2	2	no	—
46	C₁₃×H(5,𝔽₂)	—	2	2	no	—
47	C₁₃×#137	—	2	2	no	—
48	C₁₃×#137	—	2	2	no	—
49	C₁₃×#137	—	4	2	no	—
50	C₁₃×#137	—	4	2	no	—
51	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
52	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
53	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
54	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
55	C₁₃×#135	—	2	2	no	—
56	C₁₃×#135	—	2	2	no	—
57	C₁₃×#135	—	4	2	no	—
58	C₁₃×#135	D₄	1	1	yes	characteristic
59	C₁₃×#135	C₂³	1	2	yes	—
60	C₂×C₁₃×Q₁₆	—	2	2	no	—
61	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	4	2	no	—
64	C₂×C₁₃×D₈	—	2	2	no	—
65	C₂×C₁₃×D₈	C₂³	1	2	yes	—
66	C₁₃×#131	—	2	2	no	—
67	C₁₃×#131	C₂³	1	1	yes	characteristic
68	C₁₃×#131	C₂³	1	1	yes	characteristic
69	C₁₃×#124	—	2	2	no	—
70	C₁₃×Q₃₂	—	2	2	no	—
71	C₁₃×Q₃₂	—	2	1	no	—
72	C₁₃×Q₃₂	—	2	1	no	—
73	C₁₃×Q₃₂	D₄	1	1	yes	characteristic
74	C₁₃×SD₃₂	—	2	2	no	—
75	C₁₃×SD₃₂	—	2	2	no	—
76	C₁₃×SD₃₂	—	4	2	no	—
77	C₁₃×SD₃₂	D₄	1	2	yes	—
78	C₁₃×D₁₆	—	2	2	no	—
79	C₁₃×D₁₆	—	2	1	no	—
80	C₁₃×D₁₆	—	2	1	no	—
81	C₁₃×D₁₆	D₄	1	1	yes	characteristic
82	C₁₃×M₃₂	—	2	1	no	—
83	C₁₃×M₃₂	—	2	1	no	—
84	C₁₃×M₃₂	C₂³	1	1	yes	characteristic
85	C₁₃×M₃₂	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₁₆	—	2	1	no	—
87	C₂×C₁₃×C₁₆	—	2	1	no	—
88	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
90	C₁₃×#108	D₄	1	1	yes	characteristic
91	C₁₃×#108	C₂³	1	2	yes	—
92	C₁₃×#104	—	2	2	no	—
93	C₁₃×#104	D₄	1	1	yes	characteristic
94	C₁₃×#104	D₄	1	1	yes	characteristic
95	C₁₃×#101	—	2	2	no	—
96	C₁₃×#100	—	2	2	no	—
97	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	#33859	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₁₃×#41	—	2	2	no	—
100	C₁₃×#41	—	4	2	no	—
101	C₁₃×#41	—	4	2	no	—
102	C₁₃×#41	—	4	2	no	—
103	C₁₃×#41	—	4	2	no	—
104	C₁₃×#41	—	8	2	no	—
105	C₁₃×#41	C₂×D₄	1	1	yes	characteristic
106	C₁₃×#41	C₂×D₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	4	2	no	—
109	C₂×Q₈×C₁₃	—	4	2	no	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	—	8	2	no	—
114	C₁₃×Q₁₆	—	2	2	no	—
115	C₁₃×Q₁₆	—	2	2	no	—
116	C₁₃×Q₁₆	—	4	2	no	—
117	C₁₃×Q₁₆	—	4	2	no	—
118	C₁₃×Q₁₆	D₈	1	1	yes	characteristic
119	C₁₃×Q₁₆	C₂×D₄	1	2	yes	—
120	C₁₃×SD₁₆	—	2	2	no	—
121	C₁₃×SD₁₆	—	4	2	no	—
122	C₁₃×SD₁₆	—	4	2	no	—
123	C₁₃×SD₁₆	—	4	2	no	—
124	C₁₃×SD₁₆	—	4	2	no	—
125	C₁₃×SD₁₆	—	4	2	no	—
126	C₁₃×SD₁₆	—	4	2	no	—
127	C₁₃×SD₁₆	D₈	1	1	yes	characteristic
128	C₁₃×SD₁₆	D₈	1	1	yes	characteristic
129	C₁₃×D₈	—	2	2	no	—
130	C₁₃×D₈	—	2	2	no	—
131	C₁₃×D₈	—	4	2	no	—
132	C₁₃×D₈	—	4	2	no	—
133	C₁₃×D₈	D₈	1	1	yes	characteristic
134	C₁₃×D₈	C₂×D₄	1	2	yes	—
135	C₁₃×M₁₆	—	2	1	no	—
136	C₁₃×M₁₆	—	2	1	no	—
137	C₁₃×M₁₆	—	2	2	no	—
138	C₁₃×M₁₆	—	4	2	no	—
139	C₁₃×M₁₆	C₂×D₄	1	1	yes	characteristic
140	C₁₃×M₁₆	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	4	2	no	—
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₁₃×C₂²⋊C₄	—	8	2	no	—
147	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₁₃×C₁₆	—	2	1	no	—
149	C₁₃×C₁₆	—	2	1	no	—
150	C₁₃×C₁₆	—	2	1	no	—
151	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
152	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
153	#3417	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#3415	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#3290	C₂×C₁₃	1	2	yes	complemented
156	#2249	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2222	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#2221	C₂×C₁₃	1	1	yes	characteristic, complemented
159	#2212	C₂×C₁₃	1	2	yes	complemented
160	#2194	C₂×C₁₃	1	2	yes	complemented
161	#2193	C₂×C₁₃	1	2	yes	complemented
162	#2178	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2170	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	8	2	no	—
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	4	2	no	—
169	Q₈×C₁₃	—	8	2	no	—
170	Q₈×C₁₃	C₂×D₈	1	1	yes	characteristic
171	Q₈×C₁₃	C₂×D₈	1	1	yes	characteristic
172	D₄×C₁₃	—	2	1	no	—
173	D₄×C₁₃	—	2	1	no	—
174	D₄×C₁₃	—	2	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	8	2	no	—
179	D₄×C₁₃	—	8	2	no	—
180	D₄×C₁₃	—	8	2	no	—
181	D₄×C₁₃	C₂×D₈	1	1	yes	characteristic
182	D₄×C₁₃	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	8	2	no	—
189	C₂×C₄×C₁₃	—	8	2	no	—
190	C₂×C₄×C₁₃	—	8	2	no	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	—	2	1	no	—
194	C₈×C₁₃	—	4	2	no	—
195	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
196	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
197	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
199	#578	C₂²×C₁₃	1	2	yes	complemented
200	#577	—	2	2	no	—
201	#576	C₂²×C₁₃	1	2	yes	—
202	#510	—	2	2	no	—
203	#510	C₂²×C₁₃	1	2	yes	complemented
204	#509	—	2	2	no	—
205	#509	C₂²×C₁₃	1	2	yes	—
206	#508	—	2	1	no	—
207	#508	—	2	1	no	—
208	#508	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×Q₃₂	—	2	1	no	—
210	C₂×Q₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
211	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
212	C₂×D₁₆	—	2	1	no	—
213	C₂×D₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	#504	C₂²×C₁₃	1	1	yes	characteristic
215	#504	C₂²×C₁₃	1	1	yes	characteristic, complemented
216	#495	C₂²×C₁₃	1	2	yes	complemented
217	#473	C₂²×C₁₃	1	2	yes	—
218	#472	C₂²×C₁₃	1	2	yes	complemented
219	#471	—	2	2	no	—
220	#455	—	2	2	no	—
221	#454	—	2	2	no	—
222	#443	C₂²×C₁₃	1	1	yes	characteristic
223	#443	C₂²×C₁₃	1	2	yes	complemented
224	#368	C₂²×C₁₃	1	1	yes	characteristic, complemented
225	#364	C₂²×C₁₃	1	1	yes	characteristic, complemented
226	#362	C₂²×C₁₃	1	2	yes	complemented
227	#361	C₂²×C₁₃	1	2	yes	complemented
228	#359	C₂²×C₁₃	1	2	yes	complemented
229	#350	C₂²×C₁₃	1	1	yes	characteristic
230	#350	C₂²×C₁₃	1	1	yes	characteristic, complemented
231	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	4	2	no	—
235	C₂²×C₁₃	—	8	2	no	—
236	C₂²×C₁₃	—	16	2	no	—
237	C₂²×C₁₃	—	32	2	no	—
238	C₂²×C₁₃	#576	1	1	yes	characteristic
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	4	1	no	—
242	C₄×C₁₃	—	4	2	no	—
243	C₄×C₁₃	—	8	2	no	—
244	C₄×C₁₃	D₄²	1	1	yes	characteristic
245	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
246	2₋¹⁺⁴	—	2	2	no	—
247	H(5,𝔽₂)	—	2	2	no	—
248	#137	—	2	2	no	—
249	#137	—	2	2	no	—
250	#137	—	4	2	no	—
251	#137	—	4	2	no	—
252	AGL(1,ℤ/8)	—	2	2	no	—
253	AGL(1,ℤ/8)	—	2	2	no	—
254	AGL(1,ℤ/8)	—	4	2	no	—
255	AGL(1,ℤ/8)	—	4	2	no	—
256	#135	—	2	2	no	—
257	#135	—	2	2	no	—
258	#135	—	4	2	no	—
259	#135	D₄×C₁₃	1	1	yes	characteristic
260	#135	C₂³×C₁₃	1	2	yes	—
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	4	2	no	—
265	C₂×D₈	—	2	2	no	—
266	C₂×D₈	C₂³×C₁₃	1	2	yes	—
267	#131	—	2	2	no	—
268	#131	C₂³×C₁₃	1	1	yes	characteristic
269	#131	C₂³×C₁₃	1	1	yes	characteristic
270	#124	—	2	2	no	—
271	Q₃₂	—	2	2	no	—
272	Q₃₂	—	2	1	no	—
273	Q₃₂	—	2	1	no	—
274	Q₃₂	D₄×C₁₃	1	1	yes	characteristic
275	SD₃₂	—	2	2	no	—
276	SD₃₂	—	2	2	no	—
277	SD₃₂	—	4	2	no	—
278	SD₃₂	D₄×C₁₃	1	2	yes	—
279	D₁₆	—	2	2	no	—
280	D₁₆	—	2	1	no	—
281	D₁₆	—	2	1	no	—
282	D₁₆	D₄×C₁₃	1	1	yes	characteristic
283	M₃₂	—	2	1	no	—
284	M₃₂	—	2	1	no	—
285	M₃₂	C₂³×C₁₃	1	1	yes	characteristic
286	M₃₂	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₁₆	—	2	1	no	—
288	C₂×C₁₆	—	2	1	no	—
289	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
290	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
291	#108	D₄×C₁₃	1	1	yes	characteristic
292	#108	C₂³×C₁₃	1	2	yes	—
293	#104	—	2	2	no	—
294	#104	D₄×C₁₃	1	1	yes	characteristic
295	#104	D₄×C₁₃	1	1	yes	characteristic
296	#101	—	2	2	no	—
297	#100	—	2	2	no	—
298	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
299	C₂×C₁₃	—	2	1	no	—
300	C₂×C₁₃	—	4	1	no	—
301	C₂×C₁₃	—	4	1	no	—
302	C₂×C₁₃	—	8	2	no	—
303	C₂×C₁₃	—	16	2	no	—
304	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
305	#41	—	2	2	no	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	#41	—	8	2	no	—
311	#41	C₂×D₄×C₁₃	1	1	yes	characteristic
312	#41	C₂×D₄×C₁₃	1	1	yes	characteristic
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	8	2	no	—
320	Q₁₆	—	2	2	no	—
321	Q₁₆	—	2	2	no	—
322	Q₁₆	—	4	2	no	—
323	Q₁₆	—	4	2	no	—
324	Q₁₆	C₁₃×D₈	1	1	yes	characteristic
325	Q₁₆	C₂×D₄×C₁₃	1	2	yes	—
326	SD₁₆	—	2	2	no	—
327	SD₁₆	—	4	2	no	—
328	SD₁₆	—	4	2	no	—
329	SD₁₆	—	4	2	no	—
330	SD₁₆	—	4	2	no	—
331	SD₁₆	—	4	2	no	—
332	SD₁₆	—	4	2	no	—
333	SD₁₆	C₁₃×D₈	1	1	yes	characteristic
334	SD₁₆	C₁₃×D₈	1	1	yes	characteristic
335	D₈	—	2	2	no	—
336	D₈	—	2	2	no	—
337	D₈	—	4	2	no	—
338	D₈	—	4	2	no	—
339	D₈	C₁₃×D₈	1	1	yes	characteristic
340	D₈	C₂×D₄×C₁₃	1	2	yes	—
341	M₁₆	—	2	1	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
346	M₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
351	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
352	C₂²⋊C₄	—	8	2	no	—
353	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₁₆	—	2	1	no	—
355	C₁₆	—	2	1	no	—
356	C₁₆	—	2	1	no	—
357	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₁₆	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₁₃	#33859	1	1	yes	characteristic, direct product factor, Sylow
360	C₂³	—	4	2	no	—
361	C₂³	—	8	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	8	2	no	—
366	Q₈	C₂×C₁₃×D₈	1	1	yes	characteristic
367	Q₈	C₂×C₁₃×D₈	1	1	yes	characteristic
368	D₄	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	2	no	—
376	D₄	—	8	2	no	—
377	D₄	C₂×C₁₃×D₈	1	1	yes	characteristic
378	D₄	C₂×C₁₃×D₈	1	1	yes	characteristic
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	4	2	no	—
391	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
392	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
393	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	16	2	no	—
400	C₂²	—	32	2	no	—
401	C₂²	C₁₃×#576	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	8	2	no	—
407	C₄	D₄²×C₁₃	1	1	yes	characteristic
408	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	4	1	no	—
411	C₂	—	4	1	no	—
412	C₂	—	8	2	no	—
413	C₂	—	16	2	no	—
414	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#443 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3417	C₂	semidirect
2. C₁₃×#3415	C₂	semidirect
3. C₁₃×#3290	C₂	semidirect
4. C₁₃×#2249	C₂	semidirect
5. C₁₃×#2222	C₂	semidirect
6. C₁₃×#2221	C₂	semidirect
7. C₁₃×#2212	C₂	semidirect
8. C₁₃×#2194	C₂	semidirect
9. C₁₃×#2193	C₂	semidirect
10. C₁₃×#2178	C₂	semidirect
11. C₁₃×#2170	C₂	semidirect
12. C₁₃×#578	C₂²	semidirect
16. C₁₃×#510	C₂²	semidirect
23. C₂×C₁₃×Q₃₂	C₂²	semidirect
24. C₂×C₁₃×SD₃₂	C₂²	semidirect
28. C₁₃×#504	C₂²	semidirect
29. C₁₃×#495	C₂²	semidirect
31. C₁₃×#472	C₂²	semidirect
36. C₁₃×#443	C₂²	semidirect
37. C₁₃×#368	C₂²	semidirect
38. C₁₃×#364	C₂²	semidirect
39. C₁₃×#362	C₂²	semidirect
40. C₁₃×#361	C₂²	semidirect
41. C₁₃×#359	C₂²	semidirect
43. C₁₃×#350	C₂²	semidirect
44. C₄×C₁₃×C₁₆	C₂²	semidirect
98. #33859	C₁₃	direct (N × H)
153. #3417	C₂×C₁₃	semidirect
154. #3415	C₂×C₁₃	semidirect
155. #3290	C₂×C₁₃	semidirect
156. #2249	C₂×C₁₃	semidirect
157. #2222	C₂×C₁₃	semidirect
158. #2221	C₂×C₁₃	semidirect
159. #2212	C₂×C₁₃	semidirect
160. #2194	C₂×C₁₃	semidirect
161. #2193	C₂×C₁₃	semidirect
162. #2178	C₂×C₁₃	semidirect
163. #2170	C₂×C₁₃	semidirect
199. #578	C₂²×C₁₃	semidirect
203. #510	C₂²×C₁₃	semidirect
210. C₂×Q₃₂	C₂²×C₁₃	semidirect
211. C₂×SD₃₂	C₂²×C₁₃	semidirect
215. #504	C₂²×C₁₃	semidirect
216. #495	C₂²×C₁₃	semidirect
218. #472	C₂²×C₁₃	semidirect
223. #443	C₂²×C₁₃	semidirect
224. #368	C₂²×C₁₃	semidirect
225. #364	C₂²×C₁₃	semidirect
226. #362	C₂²×C₁₃	semidirect
227. #361	C₂²×C₁₃	semidirect
228. #359	C₂²×C₁₃	semidirect
230. #350	C₂²×C₁₃	semidirect
231. C₄×C₁₆	C₂²×C₁₃	semidirect
359. C₁₃	#33859	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3417	2
C₁₃×#3415	2
C₁₃×#3290	2
C₁₃×#2249	2
C₁₃×#2222	2
C₁₃×#2221	2
C₁₃×#2212	2
C₁₃×#2194	2
C₁₃×#2193	2
C₁₃×#2178	2
C₁₃×#2170	2
#33859	13

Subgroups — C13×#33859 #15720198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33859 #15720198